Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. f ( x ) = ( 2 x + 5 ) ( 3 x − 4 )
Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. f ( x ) = ( 2 x + 5 ) ( 3 x − 4 )
Solution Summary: The author explains how to calculate the derivative of the function, fprime (x), using product rule and then power rule.
Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results.
f
(
x
)
=
(
2
x
+
5
)
(
3
x
−
4
)
Formula Formula d d x f − g = d d x ( f ) − d d x ( g )
1. For each of the following, find the critical numbers of f, the intervals on which f is increasing or decreasing, and the relative
maximum and minimum values of f.
(a) f(x) = x² - 2x²+3
(b) f(x) = (x+1)5-5x-2
(c) f(x) =
x2
x-9
2. For each of the following, find the intervals on which f is concave upward or downward and the inflection points of f.
(a) f(x) = x - 2x²+3
(b) g(x) = x³- x
(c) f(x)=x-6x3 + x-8
3. Find the relative maximum and minimum values of the following functions by using the Second Derivative Test.
(a) f(x)=1+3x² - 2x3
(b) g(x) = 2x3 + 3x² - 12x-4
Find the
Soultion to the following dy
differential equation using Fourier in
transforms:
=
, хуо, ухо
according to the terms:
lim u(x,y) = 0
x18
lim 4x (x,y) = 0
x14
2
u (x, 0) =
=\u(o,y) =
-y
لو
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